The present invention relates to a method and apparatus for measuring the forming error of an object.
Some three-dimensional objects have complicated shapes, but have optically smooth surfaces and can be expressed by mathematically. Hitherto, the deviation of such a shape to a predetermined ideal shape to be formed (namely, forming error) is measured using a computer hologram method. In this method, in order to produce a hologram, a hologram figure is calculated by the computer from mathematical expressions representing the shape. An actual stereoscopic figure is drawn precisely on the basis of the hologram figure by a high-precision drawing apparatus such as an EB (electron beam) drawing apparatus. A laser beam is radiated onto the stereoscopic figure. The laser beam diffracted by the stereoscopic figure and the light reflected by the three-dimensional object overlap, so that an interference fringe is produced. The forming error of the three-dimensional object is measured from this interference fringe.
In this measuring method, a hologram must be produced and an expensive drawing apparatus is needed to produce the hologram.
There is another method of measuring the forming error of a three-dimensional object using a phase detecting system. Such a conventional method using the phase detecting system will be described with reference to FIG. 1.
A coherent light source 1, e.g., a laser generator generates a laser beam 2. The laser beam 2 enters a Michelson's interferometer 3. The interferometer 3 comprises a collimator lens 4, a half mirror 5, a condenser lens 8, and an image-forming lens 10. The laser beam 2 is enlarged to have a wider beam width and is converted to a parallel beam by the collimator lens 4. The laser beam 2 then enters the half mirror 5 at an angle of 45.degree. to this parallel beam. The incident laser beam 2 is divided into two beams. One of the beams is deflected normally by the half mirror 5 and the other is transmitted straight through the half mirror 5. The deflected beam is projected through the condenser lens 8 onto the spherical plane of a spherical mirror 9 as an object to be measured and is reflected as an object beam 6 by the mirror 9. This object beam 6 is transmitted through the condenser lens 8, half mirror 5 and image-forming lens 10 and directed to an image sensor-monitor 11. The laser beam straightly transmitted through the half mirror 5 enters a reference mirror 12 arranged in the path of this laser beam and reflected by the mirror 12. The reflected laser beam is returned as a reference beam 7 to the half mirror 5 and is deflected thereby. This deflected laser beam is then transmitted through the image-forming lens 10 and directed to the sensor-monitor 11. The interference light caused due to interference between the object beam 6 and the reference beam 7 enters the image sensing section of the sensor-monitor 11. The interference light is converted to an electric signal by the sensor-monitor 11, so that an image of the interference fringe is derived on the image display screen.
When measuring the forming error of a spherical or plane mirror by an ordinary interferometer, the forming error is obtained on the basis of the straightness of the interference fringe. When it is intended to perform a measurement with higher precision, phase detection is carried out. As shown in FIG. 1, the reference mirror 12 is equipped with a driving apparatus 13. By driving the driving apparatus 13, the reference mirror 12 is minutely moved, thereby changing the phase of the reference beam 7. A drive controller 14 drives the driving apparatus 13 so that the phase of the reference beam 7 varies in four steps at .pi./2 at a step. A memory-data processor 15 is provided between the sensor-monitor 11 and the drive controller 14. The memory-data processor 15 receives the electric signal corresponding to the interference fringe from the sensor-monitor 11, converts to a digital signal, and stores this signal synchronously with each four-step change of the reference beam 7.
When the phase of the reference beam 7 is changed in four steps, the intensity distribution I.sub.N of the interference fringe which is input to the memory-data processor 15 is: ##EQU1## I.sub.N (x,y): Intensity distribution of the interference fringe on the image display screen, namely, on the X-Y coordinate plane at the N-th change step.
I.sub.O (x,y): Intensity distribution of the laser beam, namely, the bias component of I.sub.N (x,y). PA1 .gamma.: Visibility of the interference fringe. PA1 .psi.(x,y): Phase distribution or difference of the object beam which is caused due to the forming error of the spherical mirror 9 to be measured (measured in radians). PA1 N : Ordinal number indicating the number of the change step of the phase of the reference beam 7. Namely, N is either one of integers 1 to 4.
In the above equation (1), it is assumed that the forming error is zero, that is, the spherical mirror 9 has an ideal sphere, and the .psi.(x, y) is constant. The .psi.(x,y) has a direct relation with the forming error, so the forming error can be obtained by determining .psi.(x,y). When an object to be measured is the spherical mirror 9 as in this example, the forming error H(x,y) is expressed by: ##EQU2## Where, .lambda. is a wavelength of the laser beam and K is a constant. The phase distribution .psi.(x,y) can be calculated by performing an arithmetic operation. ##EQU3## By calculating ##EQU4## using the calculated .psi.(x,y), the forming error H(x,y) can be derived. The above-mentioned arithmetic operations for obtaining the H(x,y) and .psi.(x,y) are executed by the memory-data processor 15.
According to this measuring method using the phase detecting system which has been described with reference to FIG. 1, the forming error of any planes and spheres can be very accurately measured. However, in the case of complicated objects, a measurement error is caused because the intensity distribution of the interference fringe deviates from the sine function. When an object to be measured is a complicated object, the difference between the measured value and the ideal value is obtained in order to measure the forming error. Furthermore, the error component based on the position and posture of the object is removed. Thus, the number of operations is increased, resulting in very low operating efficiency. On the other hand, in the case of a deep object, the interval of the interference fringe which is formed on the image displaying screen of the sensor-monitor 11 becomes narrow, so that the result of the measurement is influenced by the size of one pixel on the image displaying screen.
A measuring method by way of moire topography has been known as still another measuring methqd. This measuring method will be described with reference to FIG. 2. A laser beam 2 radiated from a laser generator 1 serving as a coherent light source is transmitted through a lattice 3A and enters a measuring object 9 whose forming error is to be measured. The beam light reflected by the measuring object 9 is again transmitted through the lattice 3A and enters a sensor-monitor 11. In this case, a fringe pattern image as shown in FIG. 3 appears on the display screen of the sensor-monitor 11. In the image shown in FIG. 3 curved fringes 9' are moire contour lines showing the shape of the object 9 and straight fringes 3A' indicate the lattice image. Only the curved moire contour lines 9' are needed to measure the forming error and the straight fringes 3A' become noise. A driver 13 is provided for the lattice 3 to erase the straight fringes 3A' as the noise. The lattice 3A is repeatedly moved by the driver 13 in the directions indicated by the arrows. In this case, the moire contour lines 9' do not move but the straight fringes 3A' move on the display screen. If the image on the display screen is observed for a long time, the straight fringes 3A' will be averaged and eventually erased. In other words, the noise component is removed, so that only the moire contour lines 9' remain as shown in FIG. 4 and the forming errors can be measured with a high degree of accuracy.
According to the conventional measuring method described in conjunction with FIG. 2, a hologram of the object to be measured has to be made, so that an expensive drawing apparatus or EB drawing apparatus has to be used.